For our special example given by the deformed Hopf fibration \(A_\theta \) ,
we have that \(K_\theta =K\)  and \(B_\theta =B\)  are undeformed,
hence the deformed and the undeformed associated
module functors \(E_A , E_{A_\theta } \colon {}^H\!\!{M} \rightarrow {}_{B}^{K}{M}\) 
have the same target category. Proposition REF 
proves that these two functors are already `the same'
(in the sense of naturally isomorphic) even if we do not use the deformation
functor \(\Sigma _\theta \) . Hence, our natural isomorphism in
Proposition REF  is more special and
stronger than the results from the general theory of 2-cocycle
deformations from [1]}, [2]} and [3]}.

